The most common and most likely answer to this crossword clue is the 8 letter word AFFINITY
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More clues leading to the result AFFINITY
Buddy explains!

The straight part
We know that "relationship" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case relationship = affinity.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 AFFINITY mean?
AFFINITY noun- A natural attraction or feeling of kinship to a person or thing.
- A family relationship through marriage of a relative (e.g. sister-in-law), as opposed to consanguinity (e.g. sister).
- A kinsman or kinswoman of a such relationship; one who is affinal.
- The fact of and manner in which something is related to another.
- Any romantic relationship.
- Any passionate love for something.
- Resemblances between biological populations; resemblances that suggest that they are of a common origin, type or stock.
- Structural resemblances between minerals; resemblances that suggest that they are of a common origin or type.
- An attractive force between atoms, or groups of atoms, that contributes towards their forming bonds
- The attraction between an antibody and an antigen
- Tendency to keep a task running on the same processor in a symmetric multiprocessing operating system to reduce the frequency of cache misses
- An automorphism of affine space.