If you are asking about the drive from Galway to Cong (where Ashford Castle is located), it is approximately and hour (but I would call it an hour and a half), IF you do not take the longer route thru the Connemera Region.
If it were me, if you were thinking about coming from Liscannor to then stay at Galway, then drive to Cong that next morning do your activities at Ashford, then head to back to Galway to turn in your vehicle and catching the train to Dublin................INSTEAD (if the train departure times from Galway allow), I would suggest driving on up to Cong, staying someone in/near there that night, the next a.m. do your hawk walk and tea at Ashford (book the walk in advance), THEN drive back to Galway in the afternoon to catch the train to Dublin (again if train schedules allow)
If you can swing two days in Cong, the first day you could drive from Liscannor (have lunch in Galway...the Key Street area is cute), then drive up to the Connemera region (taking the longer route), then stay overnight in/near Cong for TWO nights, enjoy your Hawk Walk, tea at Ashford, lunch or dinner at a pub in the village of Cong, spend the night, then head down to Galway late morning, catch your train to Dublin.
Staying in Galway would work, but just two road trips in the same day to get to Cong and back.
The other alternative would be to book the Hawk Walk at Dromoland Castle, which is not as far from Liscannor (during one of your four days there), then drive on up thru Doolin (see the Cliffs), The Burren, on to Galway (stay a night there), visit Key Street area, then head on to Dublin the next a.m. by train.
No real "right" or "wrong" day to do it, just a matter of how packed you would want your Hawk Walk day.