It is the first time the company, which is now facing 17 claims, has set out a specific sum for these matters. The £4m adds to an amount understood to be in the "low single-digit" millions that has already been put aside.
The newspaper publisher has previously acknowledged the ongoing impact of "historical legal issues". The latest disclosure came as the group, which owns titles such as the Daily Record and Daily Mirror, said it had performed better than expected in the half-year to June 29 and was on course to pay a dividend for 2014.
The company expects 3p per share will be paid as a dividend for this year with 5p per share for next year's performance.
However,Trinity confirmed that it is still co-operating with police over Operation Elveden - the probe into alleged inappropriate payments to public officials - and Operation Golding - the investigation into alleged phone hacking.
It added: "The group is aware of a number of civil claims from individuals in relation to phone-hacking.
"In the first half, we have provided £4million to cover the cost of dealing with and resolving claims.
"It remains uncertain as to how these matters will progress, whether further allegations or claims will be made, and (what) their financial impact (will be)."
Last week, reporter Dan Evans was given a suspended prison sentence after he pleaded guilty to two charges of conspiring to hack phones.
One charge related to his time at the Sunday Mirror between 2003 and 2005, the other to his subsequent employment from 2004 to 2010 at the News of the World.
In the interim results, Trinity said adjusted profit before tax fell 2.2 per cent to £48.2m as it increased investment and absorbed an increase in newsprint prices. The company said print revenues declined by 4.3 per cent, a lower drop than the 6.7 per cent fall in the previous year, with print advertising dipping 8.8 per cent to £108.3m.
The market for regional titles remained "difficult," it added, with paid-for dailies down 13.4 per cent. Total circulation revenue was down 1.2 per cent to £142.5m.
But digital revenues increased by 47.5 per cent year on year to £14.9m as online outlets saw average monthly unique users increase 91 per cent to 61.3 million.
Trinity also recorded a £27.5m gain for its share in the disposal of MeteoGroup by the Press Association.
Chief executive Simon Fox said: "The group continues to make good progress with the delivery of our strategic initiatives, as clearly demonstrated in the performance for the first half of 2014.
"This momentum gives the board confidence that our performance for the year will be marginally ahead of expectations."
Net debt dropped by £41m to £56m.