The approach you tried doesn't work because f[2] is evaluated before the replacement rule is applied.
An approach like the following certainly works:
Module[{fResult},
a = 1;
fResult = f[2];
a =.;
fResult
]
But that's probably too ornate for whatever you are doing given that you don't want to define an f[x_,a_].
Another approach is to define f as
f[x_] := x^2
and then to execute
If[a > 0, f[2]] /. a -> 1
or
If[a > 0, f[2],alternative] /. a -> 1
I'm sure there are lots of approaches, but which one you might use depends on the particular problem that you are coding.
