This is the term for a ruling from the UK Takeover Panel. If a potential buyer for a company is thinking of making an offer, but is not yet in a position to make a firm bid, and the approach is unwelcome to the target company, the target can ask the Panel to impose a deadline to clarify the potential bidder's intentions. If the potential bidder "puts up" it makes a firm offer: if it "shuts up" it must say it has no intention to bid and this normally bars it from making an offer for six months. 
The "put up or shut up" order is one of the best weapons available to a besieged UK company, but knowing when to use it calls for sound judgment: too soon and shareholders may miss an attractive offer for their company; too late and a company could be damaged following months of uncertainty.
The "put up or shut up" Takeover Panel rule is designed to stop predators besieging companies for an indefinite period of time. It requires a potential bidder either to make an offer to shareholders or walk away for a period of six months.