The phrase "a further setback for" is correct and usable in written English.
It can be used to describe an additional difficulty or obstacle faced by someone or something, often in a negative context.
Example: "The recent funding cuts represent a further setback for the struggling nonprofit organization."
Alternatives: "an additional blow to" or "another obstacle for".
It is a further setback for José Luis Rodríguez Zapatero, Spain's unpopular prime minister.
In a further setback for Akin, he has raised just $100,000 in an online fundraising drive that he called a message to "party bosses" about his commitment to the Missouri Senate race.
But, in a further setback for the government, executives close to the negotiations said today that the Towers-led consortium was scrambling to meet a BMW deadline to guarantee financing.
There was a further setback for the Blues when the Wales and Lions skipper, Sam Warburton, was forced off early with a nasty looking cut to his eye that was to end his day's work.
In a further setback for Rousseff, the TCU rejected a request by attorney general Luís Inacio Adams to remove the judge auditing the 2014 accounts for publicly declaring weeks ago he planned to find them invalid.
In a further setback for the credibility of ASEAN, Indonesia's foreign minister, Marty Natalegawa, had been due to fly in to chair talks between the two sides on April 25th, only for the trip to be cancelled at late notice.
Peterborough suffered a further setback when Lee Frecklington was dismissed for a second booking 10 minutes before half-time.
A recent federal court ruling invalidating his recess appointees to the National Labor Relations Board, which enforces federal labor law, will be a further setback to workers' ability to bargain for higher wages.
Andrea Orlandi scored a delightful opener after the half-hour mark before the Premier League Magpies suffered a further setback when Shola Amoebi was sent off for a second bookable offence.
Former world and European 800m bronze medallist Jenny Meadows has suffered a further setback in her bid to be selected for the Olympics after aggravating her Achilles injury.
Watford suffered a further setback when Forestieri was shown a second yellow card for diving.
