Connor formed a deadly partnership with his fellow West Indian new ball bowler Malcolm Marshall, often trying to compete with his partner for pace. Connor was a member of the 1988 Benson and Hedges Cup Hampshire team, taking two wickets in the final at Lord's. A further honour came in 1991 when Connor was again a member of the Hampshire winning team, this time in the 1991 NatWest Trophy where he took three wickets, including that of future England batsman Graham Thorpe for 93. There was call for Connor being called up to the England one-day squad, but this never materialised. Connor tasted success for a second time in the Benson and Hedges Cup, this time in 1992 when Hampshire beat Kent. Connor took a single wicket in the match, that of Mark Ealham.