Do we always need to do regression after retesting?

Retesting is required to verify that the test cases failed in previous release, are passed after the defects are fixed.
Regression is mandatory to verify all relative or dependent modules and integration tests that are intact even after defect is fixed or after change request.
You need to retest the portion of application where defect was fixed. This may be a portion of tests in regression testing. Experience says, it is safe to do regression after retest ing as to make sure that other portions of software are intact and not affected after defect fix.