1 double agent, foreign agent, secret(-service) agent, intelligence agent, undercover agent, mole, fifth-columnist, CIA man or woman or agent, MI5 or MI6 man or woman or agent; informer, informant, Colloq mole, Slang stool-pigeon, stoolie, fink, ratfink:
In those days, everyone was a spy and you could trust no one.
2 Usually, spy on or upon. follow, shadow, trail, watch, observe, reconnoitre, keep under surveillance, US surveil, Colloq tail, check out, case:
Why should anyone from a foreign government be spying on my mother?
3 espy, glimpse, spot, catch sight or a glimpse of, descry, note, notice, see, discern:
I spied him getting into a yellow convertible.