What does "suggest" mean here?

I don't know the context, but "suggested" usually means to possibly refer to something without stating it directly. So he might have been hinting at it.

It does not meant “stated.” “Suggesting” means to imply something in an indirect manner. In this sentence, the party leader is hinting that he has been removed *without actually saying* he’s been removed.

Without context, I would assume there are two people - the party leader (A) and a guy (B) who has been in some sort of political office that is a member of that party. A is saying something that could be interpreted, but does not definitely mean, that B has been ousted from whatever his position was. Something like "After our party meeting, I think we are looking forward to a new direction under new leadership." that can be retroactively fit to whatever actually happens with B.

It's kinda what he (the party leader) thinks about the situation. His assessment of what has happened. The party leader thinks that the person has been forced to leave (the party or his position, or whatever it is).

Its unlikely that the party leader told him directly (stated) that he's been ousted. A suggestion comes with a choice or an option for the recipient to think about it while a statement does not.