Councillors put their concerns to East Riding of Yorkshire Primary Care Trust chairman Karen Knapton during a meeting last week, with the question of where and when a service would be in place top of their agenda.
Plans to employ two full-time dentists in the town by April have suffered lengthy delays, with residents forced to use a mobile service or travel further afield for appointments.
A council spokeswoman said: "Feedback was given during Monday's town council meeting, and we discussed the questions raised regarding health provision in Snaith.
"As far as we're aware plans to open a dental surgery in Snaith have not moved forward for some time, and we hope Karen will now provide an answer about a location and timescale.
"This is something that has been discussed for quite a long time but I think we're starting to see light at the end of the tunnel."
Also during Monday's meeting, councillors awarded nine local groups a share of £6,000 in grants with the recipients due to be revealed shortly.
And Coun John Barrett proposed signs directing motorists to the town's free car park be installed to ease market congestion and attract more visitors and shoppers.