A strategist was a sort of an advisor who planned strategic moves.
In 2353, Kyle Riker was working as a civilian strategist advising Starfleet in its conflict with the Tholians. In 2365, he came aboard the USS Enterprise-D as a strategic attaché. (TNG: "The Icarus Factor")
According to Ma'Bor Jetrel, the Haakonian military strategists ignored calls for a demonstration test of the Metreon cascade and initiated it on the moon of Rinax, causing the deaths of 300,000 Talaxians. (VOY: "Jetrel")