The Senate Republican leadership has hired Linda Yelmini of Windsor, chief labor relations official for five administrations until her awkward departure from government under Gov. Dannel P. Malloy late in 2014, as a part-time consultant and legislative researcher. Yelmini’s hiring foreshadows an anticipated push by Senate Republican Leader Len Fasano of North Haven to intensify efforts to tighten state employee benefits and reduce long-term labor costs. As head of the labor relations office, Yelmini was responsible for negotiating labor contracts and retirement agreements.