Should I wait for Tower to provide runway exit instructions?
Note: I am assuming you are asking about US regulations.
If the tower does not give you an instruction, you should not wait for one. Leave the runway at the next available taxiway and then wait for further instructions:

4−3−20. Exiting the Runway After Landing
The following procedures must be followed after landing and reaching taxi speed.
a. Exit the runway without delay at the first available taxiway or on a taxiway as instructed by ATC. Pilots must not exit the landing runway onto another runway unless authorized by ATC. At airports with an operating control tower, pilots should not stop or reverse course on the runway without first obtaining ATC approval.
b. Taxi clear of the runway unless otherwise directed by ATC. An aircraft is considered clear of the runway when all parts of the aircraft are past the runway edge and there are no restrictions to its continued movement beyond the runway holding position markings. In the absence of ATC instructions, the pilot is expected to taxi clear of the landing runway by taxiing beyond the runway holding position markings associated with the landing runway, even if that requires the aircraft to protrude into or cross another taxiway or ramp area. Once all parts of the aircraft have crossed the runway holding position markings, the pilot must hold unless further instructions have been issued by ATC.

(Aeronautical Information Manual, emphasis mine)