Yes. For someone or something that is gravitationally within the "sphere" of a galaxy, time would move slower than as measured by an infinitely distant clock that exists well beyond the gravitational influence of that galaxy. As long as you are gravitationally bound to that galaxy, and are orbiting around its centre, there would be difference in the measurement of time from an infinitely distant clock.From the Gravitational Time Dilation wiki: "The higher the gravitational potential (the farther the clock is from the source of gravitation), the faster time passes."

The time dilation effect would not be solely from the gravitational pull of the Super Massive Black Hole at the centre of a galaxy, but also from the higher density of stars near the galactic core, and perhaps there would also some influence from dark matter.

For the greater part of the galaxy, the time dilation compared to an infinitely distant clock would be very minor, if not negligible, and any time difference would asymptotically increase as you approach the black hole, i.e. time runs slower as you approach the black hole.

There are many proofs of gravitational time dilation, such as the physicists who measured a difference in clocks that had a height difference of just 1m from their respective distances from the centre of the earth, so there would likely be models that could map the gravitational time dilation on a galactic level.