We've had this problem for a couple of years since getting a new stray. We have two neutered toms and this later one really does try to give the old one a hard time and has beaten the old one up a few times.

The problem is worst in the morning until an hour or so after they have had their meals and they settle down and around tea time, and the newer arrival can be very territorial outside.

The only answer we have is separation. They are kept apart at these times and we try to keep one inside when the other is outside. It works most of the time but playing "musical cats" as I call it (and there is a third cat around too) can be quite a game some days.