The phrase "a tough task after" is correct and usable in written English.
It can be used to describe a challenging task that follows another event or situation.
Example: "Completing the project was a tough task after the unexpected changes in the requirements."
Alternatives: "a difficult challenge following" or "a hard job subsequent to".
"That's a tough task after half a century of de-Christianization".
A draw would not have been fatal for City, but it would have left them with a tough task after drawing with Napoli at the Etihad and losing to Bayern Munich in Germany.
British Rowing confirmed that both Grainger and Thornley will "be given the opportunity to be considered" for a place in the eight, but face a tough task after the current crew earned European gold in Brandenburg.
Rattling Brady will be a tough task a week after he led the Patriots to 45 second-half points.
"Yeah, I'd love to get a crack at Novak, but Bernie is a tough task," Kokkinakis said after claiming his first-ever win at Roland Garros.
Celtic also face a tough task against Valencia after falling out of the Champions League, in which the Spaniards have been finalists for the past two seasons.
But the lack of a resolution to several pressing issues leaves lawmakers facing a tough task when they return after the holidays, with the possibility of a high-stakes showdown when the next government funding deadline approaches.
A tough task lies ahead for Atlético after a 2-0 first-leg defeat, but not an impossible one.
But getting it approved will be a tough task for Mrs May, especially after she angered MPs on Wednesday by going on television to essentially blame them for the impasse.
Ford insisted he was not facing a tough task lifting the squad's spirits after three defeats.
But Sir Alex Ferguson's men have left themselves with a tough task to even make the last eight after an entertaining clash against the fifth-placed La Liga side.
