Yes it is possible, you can well and truly build a bit of muscle whilst you shave off your love handles in order to get ready for your beach holiday, school reunion, spring break/(enter said event here).
Don't get me wrong I don't want to blow smoke up your bottom and it isn't the case that you will get shredded and also build huge amounts of muscle and end up jacked at the end of your cut but from a realistic view point when you get to the end of your shredding phase you will look strong and athletic which is what you want not scrawny and weak.
There are a few things to consider which will affect how you progress with regards to how much muscle you can actually build and here are the key points that you need to focus on in order to truly nail down a successful body recomp which in layman's terms means to shed fat and build muscle.
So the biggest aspect that dictates your progress with regards to the muscle you can build will be your training history/ your training age so basically have you trained before and if so for how long and to what sort of level. The reason this has such a huge impact is because people who have not really trained before are able to achieve what we call newbie gains, this is a one time phenomenon (I'll put an asterisk here and go back to this) where as because you have never truly stimulated your muscles with weights your body has the ability to adapt to that new stimulus and improve muscle fibre size whilst in a calorie deficit which is generally very difficult once you have stimulated those muscles multiple times BUTTT don't let this discourage you if you have trained as all is not lost.
Having trained previously or not that does not take away from the fact that to really improve your body you need to train HARD, don't expect to be in the gym just throwing around average weights and not really stimulating or working your muscles and get BIG results as that isn't going to happen as unfortunately nothing in life comes easy. Don;t get me wrong if you've never trained just doing anything yes your going to see some results but if you want to optimise your results and get the biggest bang for your buck in the shortest period of time the biggest thing I can recommend is get a quality training program and TRAIN HARD!
If you don't know where to start reach out to a fitness professional, it doesn't have to be me it can be a coach at your gym, an online coach who you follow but basically find someone who you resonate with, who's style you like and who's training style you like the look of and reach out to them and get assistance as it will make your journey 1000X easier but if not at least get a program and hit the sessions HARD!!!
Like all things your diet is a HUGE factor when it comes to getting lean and when i say HUGE i mean the most important component as if you aren't in a calorie deficit you can train as hard as you like but trust me you will not be shift any body fat. Calories are king when it comes to fat loss but when you want to recomp your body you want to ensure that your deficit isn't too severe as this will impact not only your training but also your bodies ability to build and maintain the muscle you.
A good rule of thumb is to be in roughly a 4-500 calories a day deficit so workout your average TDEE which is the amount of calories you burn a day which includes your Basal Metabolic Rate (the amount of calories you need to stay alive in a vegetative state), your Non Exercise Activity Thermogenisis which is just your daily activity which doesn't include training or gym work so things like walking, riding your bike to work etc things like that, alongside this you have your Thermic Effect of Food which is the calories burnt during digestion and your Exercise Activity Thermogenisis which is obviously your calories burnt during training and Exercise.
So if you use a good online calculator I'd recommend the bodybuilding.com one and find out your cutting calories and plug them into My Fitness Pal or an app where you can track your calorie intake and just make sure you hit those calories everyday and keep training hard.
Now what you need to do is critically analyse your feedback weekly so if you work of measurements or weight is it going the away you want or is it not? if it isn't then I'd cut off like 100 kcals and give it another week or so and see if that helps, if it does stay there until you plateau and when you do again increase your deficit by 100 more calories. I say increase hyour deficit ass there are 2 ways that you can create a deficit one of which is by using cardio such as running, cycling, rowing or swimming etc or by diet so just taking off 100kcals from your food.
Don't go too hard just wait and let your body give you feedback but remember patience is a virtue, your love handles didn't come in 2 weeks and they won't go that quickly either but the 2 key focus points that you need to focus on are your training and being in a calorie deficit!
Put these into play and trust me you will reap the rewards!
Message me to let me know how you are getting on.