Logan van Beek claimed two key wickets late on a difficult Day Two for the bowlers at The Pattonair County Ground.
Ravi Rampaul (3-80) also added two more wickets to his tally, while Matt Critchley also struck as Gloucestershire moved into a commanding position.
Centuries from Chris Dent (169) and Ryan Higgins (101) helped the visitors to a lead of 196 at the close of play, despite both batsmen falling to van Beek in the final session.
Jack Taylor will resume on Day Three unbeaten on 13, while David Payne is not out on 12, with Gloucestershire 396-7.
Having not bowled on the opening day, Fynn Hudson-Prentice made a good start on the second morning, bowling five-consecutive maiden overs.
After bringing up a half-century partnership with Dent, Hammond was caught behind by Harvey Hosein off Rampaul for a score of 36.
The hosts were unable to claim any further wickets before lunch, as Gloucestershire closed the first session on 128-3, trailing Derbyshire by 72 runs.
Rain during the interval saw play delayed until 2.10pm, and Derbyshire were quick to make up for lost time as Matt Critchley and Rampaul claimed quick wickets to leave the visitors 143-5
Higgins arrived at the crease and stopped the flow of wickets, putting on a century stand with Dent, who reached his century in 223 balls, ten of which resulted in boundaries.
Having put on 221 runs, the highest sixth-wicket partnership for Gloucestershire against Derbyshire, the pairing of Dent and Higgins saw their stand ended by van Beek, who dismissed them both in quick succession.
Gloucestershire ended the day on 396-7, leading by 196 runs with Payne (13 not out) and Taylor (12 not out) to resume on Day Three.
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