Old English ealdorman contains ealdor, derived from eald, old, together with man.
The source glosses the derived element ealdor as parent. The puzzle explicitly asks for its deeper adjective eald, not a direct two-piece split of ealdorman.
Sources
- Merriam-Webster: alderman
The deeper Old English bases are eald, old, and man; eald supplies the derived first element ealdor.
- Online Etymology Dictionary: old
Also built on Old English *eald* "old": elder, eldest
- Online Etymology Dictionary · alderman
Meanings of the older forms on the word path.