To push a loose end of a piece of clothing or material into a particular place or position, especially to make it tidy or comfortable. (Cambridge Dictionary)
To put something into a safe or convenient place. (Cambridge Dictionary)
Push, fold, or turn (the edges or ends of something, especially a garment or bedclothes) so as to hide or secure them. (Oxford Dictionaries)
If you tuck something somewhere, you put it there so that it is safe, comfortable, or neat. (Collins Dictionary)
Tuck is food that children eat as a snack at school. (Collins Dictionary)
To push in the loose end of so as to hold tightly. (Merriam – Webster)
When And How To Tuck In Your Shirt Properly.
The Texanist: Should I Tuck my Jeans Into my Boots?