There is a mention of a Carpenters Arms in Alvin Street in 1850.
I am grateful to David Drinkwater for the following information.
On the Know Your Place website is an 1852 map of Gloucester that shows position of The Carpenters Arms in Alvin Street, Gloucester. You can overlay this map with more modern ones to see that it became no. 55. Now demolished it is the entrance to The Glos Archives