TileCal, the central hadron calorimeter of the ATLAS experiment at the Large Hadron Collider (LHC), is readout by about 10,000 photomultipliers (PMTs). Earlier studies for the performance showed a degradation in PMT response as a function of the integrated anode current. A model of the evolution of the PMT response as a function of the integrated charge, based on the measurement response during the Run 2 was built. The projected loss at the end of the High Luminosity LHC is 25% for 8% of the total TileCal PMTs. These PMTs will be replaced with a newer version. A local test setup is being used in the Pisa laboratory to study the long term response of the new PMT model considered for replacement in TileCal. Furthermore, the performance of the new PMT model is compared to the old one, the current version used to readout TileCal cells. For the first time this new PMT model has been tested after integrating more than 800 C of anode current, i.e. more than the total that PMTs will have integrated at the end of HL-LHC. Preliminary results obtained from data collected in the Pisa laboratory over a period exceeding two years are given. A study is in progress aimed to understand the response degradation of the PMTs in order to disentangle the effect of loss of quantum efficiency and change in gain.