I can not figure out how 'deciding' is being used here? "The fame election management skill of the party came under stress with the party deciding to replace candidate Mr. X with Mr.Y as the candidate for contesting the election."
Look at https://www.ef.co.uk/english-resources/english-grammar/present-participle/ and scroll down to the bottom "The present participle to explain a reason". The decision is the reason why the party was under stress.
By the way, I think it should read "The famed (famous) election management skill..."