Lounger?
Lounger... take out the 3rd letter 'u' to make longer
The word is lounger. When you remove the letter u from lounger, you get the word longer.
The 9 letter word is startling. If the l is removed from startling, the word becomes starting. If one t is removed from starting, the word becomes staring. If the a is removed from staring, the word becomes string. If the r is removed from string, the word becomes sting. If the other t is removed from sting, the word becomes sing. If the g is removed from sing, the word becomes sin. If the s is removed from sin, the word becomes in. If the n is removed from in, the word becomes I.
Lounger becomes longer when the letter u is removed.
lounger
lounger
I'm not sure you got all of it. Riddles of this nature usually take the form of, "What word becomes shorter when you add two letters to it?" The answer is "short." Alternatively, "What seven-letter word becomes longer when you take one letter away?" The answer is "lounger."
"Short" is a five-letter word that becomes shorter when you add two letters.
"lounger" seems to work.
Place (locality) ... remove 'l' to get pace (tempo)
The word is chair. When you remove the c it becomes hair. Removing the C and h, it becomes air.