Context
From a novel adapted from a British political comedy Yes, Minister
And, as if becoming managing director of a huge corporation were not enough, I am also attempting to do it part-time. I constantly have to leave the DAA to attend debates in the House, to vote, to go to Cabinet and Cabinet committees and party executive meetings and I now see that it is not possible to do this job properly or even adequately. I am rather depressed.
Additional info: The novel is written in the form of diaries by the Minister (Jim Hacker) for the DAA. DAA is the initialism of a fictitious department, the Department of Administrative Affairs. In the comedy and novel, Hacker's party is the ruling party.
Reference
From Longman Dictionary:
1st usage of executive (Adjective): relating to the job of managing a business or organization and making decisions
eg: a commission with executive powers; executive body/committee etc (=a group of people who have the power to make decisions)
From OALD:
2nd usage of executive (Noun): a group of people who run a company or an organization
Oxford Collocations Dictionary: executive + noun: executive member/meeting/board
From Cambridge Dictionary:
A noun (n) is sometimes used before another noun to give more information about it. This is called a noun modifier. Adjectives (adj) come before noun modifiers
There is no adjective usage of "party" now.
My thinking
According to OALD, the conclusion seems obvious: executive in party executive meetings is a noun, which corresponds to the rule from the Cambridge Dictionary above. But is there any possibility that executive here is an adjective, meaning that the meeting is related to managing the ruling party, given that the example sentences listed by OALD mostly use "executive" as a noun referring to a body or entity rather than as a noun modifier, as follows:
The union’s executive has/have yet to reach a decision.
She is a member of the party's national executive.
She was on the executive of the Women's Social and Political Union.