Permission to chop trees down vary with councils. Ours (Western Sydney) was always against cutting down any trees whereas the council next door allowed almost all applications to do so.
Only when our council was one of a number that was sacked by the State govt and replaced with an administrator were we able to get a successful application through. So I’d get your Strata manager to check first with the council to see what are the odds of getting your application approved before actually making it.