Briefly,
1) update the prorgamme untill the date in whcih the new activity shall be commenced, reschedule, correct all out-of-sequence activities shown in the scheduling report.
2) add the new activity to the proer location in the programme, and link it.
3) reschedule, (you might get nigative float, do not panic)
4) make sure that all the up-coming activities has proper links, for example, make sure that the cricail path is really critical not due to bad linking. (some time, depsite it is not professional planning, but some contractors tend to make links just to get dates, for example, linking installing elevators with starting of ceramic tilling in bath rooms!!)
5) if the negative float still there, that is the time extenstion you as contractor might be entitled to.
6) if the activity once lined as in step 3, did not generate nigative float, so it is not in the critical path, but you still need to make sure that the upcoming activities are linked properly. who know, may be after correcting links it become critical.
7) this analysis also can prove your acceleration cost, document any cost you encountered to bring back the project in-line.
As your post only addressed a new activity, I am assuming that it is due to variation order from the client.
Also, the above steps did not consider the analysis of con-current delays, in whcih the Contractort might be delayed in another area, that is another story.
In addition to all that, you have to read the contract very well in this area, check what is contractually requiered by you to prove your entitlements.
Hope thats help