The building above is mentioned by Pevsner in the first edition as 14 - 18 St Mary’s Street and described as “with a pedimented Georgian doorway, but it is a house of c.1500 and has three oriel windows with original sills. They illustrate the Slaughter of the Philistines by Samson, Samson and Delila, a man (Hercules?) wrestling with two dragons, three shields supported by putti, and mermaids." James Bettley, in his Third Edition revision adds to those last few words as follows "… three shields supported by putti, a bust of the Virgin Mary and mermaids." He goes on to state "Evidence at the rear of an external first-floor gallery, suggesting that it was originally a hostelry connected with the priory opposite." There is no mention here of a gildhall but it is not unknown for hostelries by a church to have been one.
However, someone locally thinks it was a Guildhall as evidenced by the plaque on the building to the right of the Georgian doorway, seen below - but note that this implies a craft guild and not a religious or parish gild. It could, of course, have had associations with both.
The listing here says it was considered to have been a private residence by Suckling (pdf downloadable from Sources), though often supposed to be connected with the Nunnery on the opposite side of the road. There is no mention of a guildhall here either.
I have not seen any corroborating evidence from Suffolk historians so this is an unconfirmed possible gildhall or more likely a church house where one or more gilds met.
The windows are shown below.
For information on buildings mentioned in the Pevsner guide to Suffolk in this location see pevsnersuffolk.co.uk