Everything I'm about to say has probably been stated before, but I'm going to add it anyway.
1. Continue with your Main Scenario Quests (MSQ), trust me you won't be running out of these any time soon and they give pretty significant EXP. I also think they now give level 50 armor if I'm not mistaken? It's been quite a long time since I've done them...
2. Run your daily roulettes, specifically Leveling Roulette. You will get a significant amount of EXP from your Roulettes on a non-level capped character. Before level 50 you'll only really have access to your Leveling Roulette and the Guildhest Roulette (if you've unlocked Guildhests anyway). Guildhests are fast, but don't reward much EXP if you're past 40, so they're not a super viable way for leveling up. But they do give Grand Company Seals if you need those!
3. Unlock your Challenge Log if you haven't already. The Challenge Log resets every week on Tuesday and it has lots of ways to earn EXP (even for crafters and gatherers too!).
4. FATEs can give pretty decent EXP. Some people grind out FATEs to level, though if this is your first class I really wouldn't recommend over doing it. There is a Challenge Log bonus for doing FATEs and they can be done while in queue for a dungeon (just don't join any parties or it'll drop your queue!). The best spot to do FATEs from 45-52 is Northern Thanalan and there is usually quite a few people (and bots) grinding FATEs there.
5. Make sure you eat food! Almost every food item in the game gives an EXP boost and it's 3%. The boost applies to mob EXP mostly, but every little bit helps! You can get some very cheap food from various vendors in the world, I like to visit the Culinarians' Guild myself and pick up milk (because my character is a Miqo'te and I think I'm hilariously witty getting milk for my cat...).
6. Do your Hunting Logs! These give a lot of EXP and Grand Company Seals.
I came across a little guide that has various things you can unlock at certain levels (including emotes, minions, and other options such as the Challenge Log, dye system, and glamor system). There are a lot of dungeons between level 50-60 so this will help you find everything very easily. I highly recommend keeping this link bookmarked. Though I would like to point out that the Binding Coil raid series is optional and not something that many people run anymore.
Hope that helps! Happy leveling and good luck, OP!