The most common and most likely answer to this crossword clue is the 2 letter word RT
R
T
Buddy explains!

The straight part
We know that "Diminutive Cabinet Minister" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case diminutive cabinet minister = rt.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 RT mean?
RT noun- A message reposted or forwarded in this way.
- Straight, not bent.
- Of an angle, having a size of 90 degrees, or one quarter of a complete rotation; the angle between two perpendicular lines.
- Of a geometric figure, incorporating a right angle between edges, faces, axes, etc.
- Complying with justice, correctness or reason; correct, just, true.
- Appropriate, perfectly suitable; fit for purpose.
- Healthy, sane, competent.
- Real; veritable (used emphatically).
- All right; not requiring assistance.
- Most favourable or convenient; fortunate.
- Designating the side of the body which is positioned to the east if one is facing north. This arrow points to the reader's right: →
- Designed to be placed or worn outward.
- Pertaining to the political right; conservative.
- A course or way which is traveled or passed.
- A regular itinerary of stops, or the path followed between these stops, such as for delivery or passenger transportation.
- A road or path; often specifically a highway.
- One of multiple methods or approaches to doing something.
- One of the major provinces of imperial China from the Later Jin to the Song, corresponding to the Tang and early Yuan circuits.
- A specific entry in a router that tells the router how to transmit the data it receives.