The position became vacant after incumbent deputy chairman Trevor Johnson informed board chairwoman Francisca Griffin he was standing down from the position for personal reasons.
Mrs Goldsmith was elected unanimously and unopposed in a vote of board members at a meeting of the community board on Thursday night.
She was elected to the board last August in a by-election after the death of longstanding board member Jan Tucker.
"I never expected to be given the role being so new on to the community board, but I’m really enjoying it."
Mr Johnson said there was no disharmony behind his decision to step down, but he felt it was the right time to move on.
He would not be standing again in this year’s local body elections after 24 years serving on the body.
After her election Mrs Goldsmith thanked her fellow board members and said she had very big shoes to fill.
"I only take a size 10," Mr Johnson replied.
