Improve adhesion between PC and TPE

There is a bit you can do to help improve adhesion between PC and TPE; two materials that don't typically love each other. I am working on a fix right now on one of our products having just this problem.

Make sure the material has been dried properly to obtain the best adhesion possible (which may not be great).
I believe you should expect better results in a two shot process as the initial shot is still warm when it receives the TPE attaining a better bond. In an insert mold operation, the part is rarely warm and sometimes has had the opportunity to take on moisture if it has been sitting around.
If you don't need the impact strength of PC, you might want to try a PBT/TPE or a PC/PBT and TPE overmold. We have seen much better results with this formulation.
Check with your vendor. Different vendors offer different compounds within the TPE that will allow the elastomer to achieve better adhesion to PC. Sometimes they work and sometimes they don't.
Make sure that your second injection or overmold temperature is set correctly.
Finally, make sure that your color carrier resin in your materbatch is the appropriate base material. Many times, the base material in a masterbatch is just some inexpensive material that the company uses because it is being used at a 50:1 ratio.

I always try to use PC as a base carrier resin in case. Immiscible carrier resins can inhibit adhesion. The important still to point out is the gate location and type of gate consideration for insert molding:

to ensure a flow path that will yield optimum adhesion
At the heaviest cross section, to facilitate part packing and minimize voids and sink
to minimize obstructions in the flow path (flowing around cores or pins)
to minimize jetting (> 0° angle injection in thin-walled components)
part packing and gate removal or vestige depending on different gate types

At least provide mold venting (0,01-0,025mm) to avoid air trapping between TPE and OM component.
Looking now to many different kind of TPE materials (Santoprene from Exxon Mobil is an EPDM/PP chemical cross linked matrix), you will definitely target a huge varity of material combinations. Differences between TPE-V and TPE-S compounds occure in

Flow length/viscosity is very shear dependent on SBC compounds, testing with spiral flow before
Melt temperature
good adhesion properties to various thermoplastic substrates/EPDM-PP compounds are limited due to chemical X-linking.

Basically the fundamental bond of GLS TPE over the rigid substrate can be provided by a combination of molecular adhesion.