Well, it's not like you have a choice now, is it? If *My* slave were to try and tell me that he wasn't okay with me having a boyfriend, he'd be in chastity for a month.
I'm pretty sure your ex-girlfriend would do the same if not worse to you. Imagine being in chastity to your ex?! What if she promised to let you out but then left the key at her boyfriend's house? Could you handle that, boy?
She might make you serve her boyfriend too, y'know. It's something you should be prepared for. It might just be demeaning little things just being made to clean his shoes, or cleaning his apartment. Or it might be serious things like *cleaning up* after him. Whatever your ex says, GOES.