The most common and most likely answer to this crossword clue is the 8 letter word WORSHIPS
I've seen this crossword clue in The Daily Telegraph
W
O
R
S
H
I
P
S
Buddy explains!

The straight part
We know that "Dignitaries" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dignitaries = worships.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 WORSHIPS mean?
WORSHIPS noun- The condition of being worthy; honour, distinction.
- The devotion accorded to a deity or to a sacred object.
- The religious ceremonies that express this devotion.
- (by extension) Voluntary, utter submission; voluntary, utter deference.
- (also by extension) Ardent love.
- An object of worship.
- Honour; respect; civil deference.
- (chiefly British) Used as a title or term of address for various officials, including magistrates
- To reverence (a deity, etc.) with supreme respect and veneration; to perform religious exercises in honour of.
- To honour with extravagant love and extreme submission, as a lover; to adore; to idolize.
- To participate in religious ceremonies.