The PRI is just the regimental shop. They usually sell a range of regimental items such as plaques, watch-straps, sweatshirts etc. along with various bits and bobs to make your life on ops or exercise more comfortable.
President of the Regiment Institute Shops
Mr. Roger Williams: To ask the Secretary of State for Defence what guidance his Department gives to commanding officers on (a) appointing external commercial businesses to run President of the Regiment Institute shops, (b) the profit margins which such businesses should charge on their sales and (c) overhead costs. 
Derek Twigg: President of the Regiment Institute shops are charities, of which the unitsâ Commanding Officer is the Managing Trustee. Instructions on the running of PRIs are not issued by the Department as the unit Commanding Officer is fully responsible for the running of their PRI as the Managing Trustee. However, they should be run in accordance with Service Funds Regulations and Defence Council Instructions General 3/2005.
The Commanding Officer may appoint any individual or organisation to manage the PRI, and may set whatever profit levels they see fit. Overhead costs are advised by Defence Estates and include licence to occupy, utility costs and ensuring adequate insurance is taken.
The PRI is the term given to the principle non public fund in a regiment. The fund is used to subsidise welfare projects in the regiment and is maintined by charity fundraising and by running various trading activities such as sticky bun and sports kit shops, typically selling regimental T shirts etc...
I think the PRI used to get a kickback from the NAAFI as well at one time..
The term is archaic as there is on such thing as the "Regimental Insititute" ot a president anymore... The PRI is the responisbilty of the CO.