Here's some guidance from Jakub Marian providing a nice rule for using the word "future" as an adjective or a noun:
When ["future" is] used as an adjective, it doesn’t take any article itself; it is preceded by the article of the noun it modifies ....
When “future” means “the time or the events that will come after the present”, it is always used with the definite article.
According to this rule, "Fridays for Future" represents improper usage because it refers to "future" as a noun but does not include the definite article.
As for your specific application, you should use the definite article in both cases:
- A Summit for the Future over A Summit for Future
- A Summit for the Future of Spin Fishing over A Summit for Future of Spin Fishing
Does the rule apply to other noun/adjective pairs?
I got some noun/adjective pair words from this Q&A. Let's see how the rule works on other noun/adjective pairs in regular sentences:
- "I'm preparing for the future" (noun) vs. "I'm preparing for future thunderstorms" (adjective)
- "I did it for the good of all people" (noun) vs. "I did it for good luck" (adjective)
- "I think about love in the abstract" (noun) vs. "I speak in abstract language about love" (adjective)
This applies also when making an adjective into a noun:
- "The land of the free and the home of the brave" (adjectives functioning as nouns) vs. "The land of free people and the home of brave people" (adjectives)
NOTE: this does not apply when we take generic nouns (sun, earth, man, power, patriarchy) to make specific nouns (the Sun, the Earth, the Man, the Power, the Patriarchy).
Does the rule apply to slogans?
Slogans don't necessarily have to follow the rules of proper grammar.
"Fridays for Good" sounds like a perfectly normal slogan, although it breaks the rule above. "Fridays for the Good", the "correct" slogan according to the rule, sounds antiquated to my ears.
Perhaps "Fridays for Future" will sound normal in 100 years, and "Fridays for the Future" will be a weird relic of 21st-century English speakers.
Caveat: "In Future" in British English
Jakub Marian showed that British English differs from American English in that sometimes you can drop the article, which changes the meaning of the phrase:
Human beings will live on the Moon in the future. (American and British English)
(Human beings will live on the Moon at some point in the future.)
Human beings will live on the Moon in future. (British English only)
(Human beings will live on the Moon from now on.)