"Help close off one town in Perugia..." = assist. Anything to do with San Sisto which is near Perugia??
This next clue 'ran on' from the above:
"...old Pope's living in it" = urban. Something to do with Urbi/Orbi??
"Islands are scattered about rear" = raise. All I can suggest is I for island and an anagram of Arse (rear) but I don't think that'll be it somehow...
"Gem, iridescent one cut into last third of quartz" = topaz. I'm happy with the TZ but not the OPA.
"Engineers unwell? Call again." = redial. Just the dial bit I can't see.