At the opening, Gene Vincent perhaps thanks first label (5,3)
I believe the answer is:
price tag
'label' is the definition.
(price tag is a kind of label)
'at the opening gene vincent perhaps thanks' is the wordplay.
'at' says to put letters next to each other.
'the opening' says to take the initial letters.
'vincent perhaps' becomes 'Price' (actor Vincent Price).
'thanks' becomes 'ta' (UK informal version of 'thank you').
The first letter of 'gene' is 'g'.
'price'+'ta'='priceta'
'g' put after 'priceta' is 'PRICE TAG'.
'first' is the link.
(Other definitions for price tag that I've seen before include "shows outlay required" , "What a ticket may show" , "Label indicating cost" , "Cost of a project, perhaps" , "Indication of cost" .)