Prayer answered after long time..

There are several..... I'll let you look 'em up......
The birth of Samuel.
Zacharius in the NT and the birth of his son.
The teacher who had prayed for a long time that he would see Jesus and did.
Daniel, repenting for the sins of his people and looking forward to the day when God would return them to Jerusalem.
I don't recall if this is specific or more implied..... but Moses in the wilderness, praying for the people, God brought them 40 yrs of judgement and experience in conditions of desolation to discipline them as to faith and the daily delievery on his provisions in spite of a harsh and unyielding environment in regard to productivity and survival.
Jacob's prayer that his people would leave Egypt one day.
The delay in judgement for Ninaveh when they repented after Jonah's preaching.
The birth of Jesus..... No doubt there were some praying and looking for the messiah for a while before his birth.
Timothy's kins women who prayed for him while raising him, answered when he accepted the call to be a servant for the gospel of Jesus Christ.
The fullfillment of Samson's parents prayer at the ending of his life.
The blessings (and prayer) of Israel (Jacob) for his children.
The fasts and prayers of Daniel asking for a vision.... the response and prophecies delivered to him which would not be fulfilled in his day nor understood until their time came.
The final prayer of John the revelator "Even so come Lord Jesus" to which we look forward to with certainty and hope.


I'm sure in some of these you'll find some prayers answered after various periods of time.
There may be better examples... but these come to my mind. I'm not sure if all fit, but surely you'll find some examples.

 

Not in the Bible, but the prayers of St. Monica for the conversion of her son, Augustine, were answered after many years and just prior to her death. Augustine went on to be one of the greatest of the early church fathers.