BrowserUk's approach is fine (of course!), but just to elaborate what was wrong with yours:

• Your match ($AP_numClients[$x][0] =~ /$AP_numClients[$x+1][0]/) is the wrong way round.  The shorter (sub)string should be on the pattern side — i.e. swap $x with $x+1 index.
• You should generally quotemeta search strings in a pattern, if they contain meta-characters ("." here).
• The @newArray would better be populated using push instead of with the same index ($x) that you use for the original array (as you have it, you'd get "undef" holes in the new array).

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