Now the idea is that him being a former member of Star Fleet get's held over his head a lot like in the middle of a battle an enemy Captain will say "You were once one of the honored Captains in Star Fleet now look at you. You've become a disgrace to your family name."
and "It's sad you could have been one of the greatest Star Fleet captains."
I'd say that rather than taunting your character in the middle of the battle, its this kind of thing that leads your pirate to do a Han Solo and take the first shot.
Now here's my problem. What's better for him to have been an ex-captain that fell from grace or a fallen ex-recruit that once showed a lot of promise?
I'd say go for someone who was at most a Lieutenant Commander, though destined for a captaincy, before whatever event saw him/her kicked out of Starfleet. That way you could have old rivals from the fleet referring to them by their old rank rather than 'Captain'.
I would want to know why a once-respected Star Fleet captain turned to piracy. It seems to be a total 180 degree turn considering that pirates are pretty much the scum of the universe. Explaining such a change would make for an interesting story. Is he/she truly a bad guy? Is he/she actually working for Star Fleet Intelligence or other covert agency? Or, perhaps he/she is seeking someone/something and piracy was the only avenue for finding it?
You should listen to this old Border Dog, he knows a thing or two about pirates
Knowing the reason behind your character's departure from Starfleet would be of benefit. Was it because of something they did: disobey orders, punch their CO, get caught doing the deed with the sector commander's daughter, neglect their duties that led to the deaths of others. Or was it more a reaction to events: they resigned in protest to the actions of others, forced into it to save face, suffered a personal loss that made them question their choices.