Republican Senate

The Senate was a primarily advisory body of elite and wealthy Romans that was made up of three hundred Senators (from the latin word for "old man"), whose main function was to issue "decrees" called consultum or senatus consultum.

consulti''
These decrees had no legal weight, but were used to represent the consensus view of the Senate or, more accurately speaking, the views of the several princeps, who were powerful senators who had the votes of many others.

The true "government," as we think of it today, was in the cursus honorum, as only elected officials and voting assemblies had the right to (1) propose and (2) enact legislation.

Tribunes of Plebs
Generally, the office of Tribune was used as a check against patrician power in the Senate (where it was practicallly absolute) and in the upper offices of the cursus honorum, at least in the early Republic'''. Eventually the Tribunes became complicit with the Senate, especially throughout the 3rd and 2nd centuries''', not putting forth laws without a decree in it's favor.

This was all to change with the active careers of Tiberius Gracchus and Gaius Gracchus.