What is required of one who swore to do something at a specific time, but did not do it at that time?

If you swore to do ‘umrah during the month of Ramadan, but when the month ended you had not done ‘umrah, then you have broken your oath and must offer expiation.

Ibn Qudaamah (may Allah have mercy on him) said: If the oath was to do something and you did not do it, and that was an oath that was connected to a specific time indicated either by the words uttered or the intention, or implicitly, then that time passed without doing anything, the oath has been broken and expiation must be offered. End quote from al-Mughni (9/494).

You do not have to do anything except offer expiation.

Expiation for breaking an oath is freeing a slave, or feeding ten poor persons, or clothing them. Whoever is unable to do any of these things must fast for three days, because Allah, may He be exalted, says (interpretation of the meaning):

“Allah will not impose blame upon you for what is meaningless in your oaths, but He will impose blame upon you for [breaking] what you intended of oaths. So its expiation is the feeding of ten needy people from the average of that which you feed your [own] families or clothing them or the freeing of a slave. But whoever cannot find [or afford it] – then a fast of three days [is required]. That is the expiation for oaths when you have sworn. But guard your oaths. Thus does Allah make clear to you His verses that you may be grateful”

[al-Maa’idah 5:89].

See also the answer to question no. 45676.

And Allah knows best.