Yes. you will need a permit for sure from the copyright owner of the song and recording copyright owner. This might not be a feasible step, as the owners may refuse or ask for huge fees. You also, need to put in consideration checking if the copyright still applied to this work or not, where many songs recorded in the 1960s or earlier have been considered a public domain, and anyone can use them.
In case you are unable to get permission for the song, or it is not in the public domain, you can use it under the right of fair use as long as you are using a short part of the song and don't make a profit from it or harming the value of the song.