This is a pretty normal beginner time. I remember after doing my first kilo (also around 1:23, haha!) I realized I didn't go nearly hard enough. At this point, more than any specific advice, I'd advise you to just really practice "getting it all out" on the track. Roadies have a kind of built-in limiter compared to track sprinters, and you really have to train your brain and body to overcome that and really go for it. This took me a while, and honestly, it's part of every training session even now (10+ years later).
Other than that:
Squats, deadlifts, pull-ups and bench are the minimum you want to hit in the gym
Starts on a track bike, at the track or on a safe section of concrete
Flying 100's, 200's and longer to get your speed.
Rolling laps, 500's, 750's to get you across the line.
All these should be maximal efforts.