Extending my residence permit

Hi, Jane. You mean you have both resident permit and visa at the same time?
It is a little bit strange. In general, you can use your new one together with a resident permit application, a recent taken photo, physical examination form, accommodation registration printout from the local police, school introduction letter and the fee to apply in the local Exit-Entry Adminstration to apply the resident permit. The form permit is suggested to take.

I mean I have a residence permit in Gansu but it expires 3rd February 2015, however I will stay here until 26th February before I move to Chongqing. Can I apply for a tourist L or extend my residence permit until I get a new one in Chongqing?

Applying a new Tourist L may not be so easy within China. If you can provide supporting documents, you may try to extend your current resident permit.
Personally speaking, you are suggested to go to the local Exit-Entry Adminstration Bureau for asking a more and better solutions. Anyway, good luck ~