This question has no answer because 'a(t)' is a parameter of the FLRW model, which does not apply within a bound system such as a galaxy. Asking what the FLRW 'a' is inside a galaxy would be like asking what is the radius of an ellipse.
The FLRW model assumes perfect homogeneity of the universe, but a galaxy is by definition a region in which the homogeneity assumption does not apply.
The question we can ask, that does make sense within a galaxy, is:
'What effect do the factors that make the universe's expansion accelerate have within a galaxy?'
The answer to that is most likely reached via analysis of the impact of a nonzero [itex]\Lambda[/itex] on the curvature of spacetime within a galaxy. My facility with tensor equations is regrettably way below the level necessary to answer that question. But it seems reasonable to be confident that the answer is not 'none whatsoever'.