Problem with getting on with the Thieves Guild restoring

Solution 1:

Each of the four cities you can run the special jobs in (Markarth, Solitude, Windhelm, and Whiterun) only requires five side jobs completed to unlock the special job. But those side quests need to be performed in the correct city, and depending on the type of job you take, Markarth can be pretty rare; there are about half to two-thirds as many valid targets in Markarth as any of the other cities for each of the Heist, Sweep, Shill, Burglary, and Numbers jobs. Even with as many side jobs completed as you have, it's entirely possible very few have been in Markarth.

If you need more Markarth side jobs, one thing you can try is to save while getting the quest, then reload until you get Markarth; it's usually what I do anyway to get Delvin and Vex to give me two quests in the same city to save time. This can take a while, though; I once reloaded about seventy times before a Numbers job came up Markarth.

Another option might be to switch to Bedlam or Fishing jobs. I haven't run them as much, but I have found that they distribute targets a bit better. The caveat here, though, is that if you have the Dragonborn expansion, Raven Rock will be added to the list of valid locations for those, tipping the odds back a bit against Markarth.

If you know for a fact that you have completed enough side quests specifically in Markarth, I'm afraid you've probably hit a bug. We've had questions about a situation like that before, and the solution so far seems to come down to using console commands on the PC to force the special job to start, or else reloading an earlier save on console versions of the game. You may also want to make sure you've updated the game fully; Bethesda fixed plenty of bugs over the course of the updates.