The most common and most likely answer to this crossword clue is the 4 plus 7 letter word BACK NUMBERS
I've seen this crossword clue in The Guardian
B
A
C
K
N
U
M
B
E
R
S
Buddy explains!
The straight part
We know that "old-fashioned types" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old-fashioned types = back numbers.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.