In a biblical passage I am studying, I noticed that the accused was given a short span of time in order to fix the problem he had caused. This idea (granting time to correct the situation) is important for my study and I want to include it in the index. Is there a word (or short two word phrase) that has this meaning?
You might want to try grace period, which, since you are talking about a bible passage, would have a nice double entendre.
I believe this is legally referred to as a remedial period.
An example of this usage can be found in this recent amendment to the Americans with Disabilities Act.
A person may be put on notice, for a definite or indefinite period, generally implying the consequences of not complying with and probably also the salutary effect of compliance.
A delinquent employee is put on notice that if does not rectify the situation, action would automatically follow. The notice period may form part of the notice, the completion of which without the condition being fulfilled satisfactorily would trigger consequential action.
Consider hang time, "how long something stays in the air" to describe the brief interval between when a manager is fired and actually escorted off the premises. One meaning noted in Wikipedia is "In some first-person shooters, the length of time a player flies through the air as the result of a grenade jump".
Also see delay synonyms, which include deferment, moratorium, postponement, reprieve, stay, and some of their synonyms in turn, like suspension, with useful synonyms in turn like hiatus, abeyance, and more.