There are ten definitions below. The answer to each of the definitions from two onwards is an anagram of the previous answer with one letter added. So SPOT could be followed by POSIT; that is, SPOT + I rearranged.
1. The perpendicular pronoun
I
2. The ratio of a circle's circumference to its diameter
PI
3. Nickname of former Speaker of the House Thomas P. O'Neill
TIP
4. A narrow piece of land formed by longshore drift
SPIT
5. Walks or runs with quick light steps
TRIPS
6. Alternative term for handwriting
SCRIPT
7. Muscle having three points of attachment
TRICEPS
8. An archaic word for Recipes
RECEIPTS
9. The most spine-chilling
CREEPIEST
10. Central points of earthquakes
EPICENTRES
Pleasingly each successive answer starts with a different letter, and is a "proper" anagram of the previous answer.