The most common and most likely answer to this crossword clue is the 8 letter word SUFFRAGE
I've seen this crossword clue in The Daily Telegraph
S
U
F
F
R
A
G
E
More clues leading to the result SUFFRAGE
- Mostly stand over tabloid franchise
- Without hesitation, put up with anger — it’s sort of right
- Vote to rewrite gaffes, interrupted by Unionist and Republican
- Fill with anger, having been denied essentially vital right to vote
- Conversely, America and France took time about female right to vote
- Franchise hurt, losing energy over time
- Pundit receiving silly ruff for voting right
- Argues irrationally about fine fellow’s franchise
- Allow doing away with European era voting rights
Buddy explains!

The straight part
We know that "sort of right" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sort of right = suffrage.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SUFFRAGE mean?
SUFFRAGE noun- The right or chance to vote, express an opinion, or participate in a decision.
- The right to vote for elected officials in a representative democracy.
- A vote in deciding a particular question.
- A prayer, for example a prayer offered for the faithful dead.
- A short petition, as those after the creed in matins and evensong.
- Aid, intercession.
- Testimony; attestation; witness; approval.