The easy answer is Yes, but it is contingent on several things. You work as a say Clerical Officer in UCD and you move to Cork City Council to work there as a Clerical Officer you can be given the benefit of your service as to attaining the next due increment. Your pension entitlement is brought also.
But, let's say you are doing Contract work in UCD as a Clerical Officer (or working in a summer job) and you make the same move, the chances are that you will be given no credit towards increment or pension. Much depends on your new employer and even your old employer.
Also, if you work as a Clerical Officer in UCD and take up appointment in CCC as a higher grade, you would be given credit towards your pension, but you might not get the incremental credit in the higher grade. Again it depends on your new employer.