One Paul song from Sgt. Pepper features session clarinets and a vaudeville sound. It is...

a. "Sgt. Pepper's Lonely Hearts Club Band"
b. "Getting Better"
c. "Lucy in the Sky With Diamonds"
d. "With a Little Help From My Friends"
e. "When I'm Sixty-Four"

  E. "When I'm Sixty-Four"

Explanation:  This famous Beatles album was released in 1967 under the full name Sgt. Pepper's Lonely Hearts Club Band. The already well-known creative duet of the band Lennon & McCartney, where they both contributed to the quality of the songs with their distinctive talents. So one of Paul's songs on this album where the clarinet is clearly heard as well as the vaudeville sound is "When I'm sixty four", which Paul himself sang on the album. It should also be said that when it comes to singing, Lennon and McCartney were as often singers as they did songs. Generally, in the song, Paul wonders if the woman will be still by his side when he is sixty-four.