When I replaced the starter in 1992 chevy suburban the small wire that goes to the cylenoid is it supposed to have constant power?

If the wire goes to the alternator, then yes. The wire from the starter relay that goes to the "S" terminal of the solenoid should not be hot. There should be a large hot wire from the battery but there may also be a hot wire from the back of the alternator. These 2 would both go on the large post of the solenoid.

The small wire should only have power when the ignition switch is in the start position. There should be no power any other time. The small wire is what energizes the solenoid which closes a set of contacts which allows power to flow to the starter motor and crank the engine over.

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