The club released a statement earlier this month condemning the actions of the unnamed players who flouted restrictions .
Those involved have now been fined and issued with a written warning about their conduct.
The incident took place when West Yorkshire was under Tier 3 of the Government's Covid-19 restrictions.
Tier 3 measures, classed as "very high risk" prevent people from mixing, indoors or outdoors, with people they do not live with or who they are not in a support bubble with.
Trinity say they consider the matter closed, with the fines donated to the Wakefield Hospice.
A club statement read: "Following the incident on New Years Eve, the club has now completed its investigations and discussions with the players concerned.
"All those involved have admitted they were wrong and have apologised, not only to the club but to the wider public.
"They recognise that they are role models in society and all our players realise the gravity of the Covid-19 situation right now.
"The players involved have been fined and given written warnings as to their future conduct.
"The monies will be donated by the club to Wakefield Hospice, a charity close to the club’s heart and one that does so much for the people of Wakefield. The club regard the matter as now closed."