Smith, who was unbeaten on 111 overnight, moved to 234 not out by the time Surrey were eventually bowled out for 603.
The 21-year-old shared a stand of 244 with Clark, but that didn't prevent Gloucestershire from putting on an impressive response - scoring 86 runs without loss.
Despite the positive start, the hosts will kick off day three trailing by 517 runs in the first inning.
Here, Planet Sport takes a look at the rest of the action accross County Championship One.
Essex in trouble after second day
Ben Sanderson exposed a gaping hole in the fragile Essex battling line-up as four blistering wickets backed up Luke Procter's marathon century to put Northamptonshire in command.
The pace bowler put on a superb display as he found a succession of edges, including Sir Alistair Cook's, as Essex were reduced to a mere 95/8.
Earlier in the day, Northamptonshire added 157 to their total as Procter spent six hours at the crease. The 33-year-old scored 113 runs as his side reached a total of 390.
Hampshire and Lancashire clash finely poised
A superb bowling display from Keith Barker has set up an intriguing third day in a closely contested match between Hampshire and Lancashire.
The 35-year-old produced his second five-wicket haul of the season to help secure Hampshire a six-run first inning advantage as the visitors were dismissed for 240.
Phil Salt and Tom Bailey produced half-centuries on the second day, before Hampshire closed on 103 for three.
The hosts lead by 109 runs with 7 wickets remaining in the second inning.
England hopefuls shine for Yorkshire
Yorkshire Dawid Malan and Harry Brook - two men hoping to force themselves into the England squad - produced impressive centuries as Yorkshire fought back against Kent at Headingley.
The visitors were on 227/4 but endured a late collapse and finished on 291 as Haris Rauf enjoyed his career-best performance of five for 65.
Yorkshire's fight back got off to a stuttering start as the home side lost three wickets for just 23 runs. However, Malan's 152 and Brook's 131 (not-out) moved the hosts to 326/5 at the end of the second day.
Yorkshire currently lead by 35 runs with five wickets remaining in the first inning.
Long way back for Warwickshire
Following a dreadful start to the season, Somerset finally have something to shout about as their bowlers put them in a commanding position against champions Warwickshire.
Josh Davey, Craig Overton and Lewis Gregory all took two wickets, while Jack Brooks, Tom Abell and Jack Leach each weighed in with one apiece.
Warwickshire, who were looking to reply to the hosts' first innings score of 458, could only manage a measly 197 for nine.
The visitors trail by 261 runs with one wicket remaining in the first inning.
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