I absolutely love the kind of aesthetic prevalent in both modern-day and 60s/Cold War spy TV-shows, but the closest I could find was the Casino aesthetic... So proposing:
Colors/clothes: red, white, black, metallic accents; trench coats, faux fur mink coats, leather jackets and gloves, bold statement sunglasses/jewelry/watches (just subtle enough not to draw any attention), suits, leather briefcases, clothing with 60s & 90s elements in general; classy, maybe with a modern twist
Music: Jazz, Blues, Saint Motel, Bond movie OSTs, Unloved, (60s) French(-inspired) Alternative
Series/Movies: Killing Eve, Man from U.N.C.L.E, Tinker Tailor Soldier Spy, From Russia with Love (any Bond movie, really), Red Sparrow, Le Samouraï, Da Vinci Code, Alex Rider (the 2020 ver.)
Books: anything crime fiction, Bond novel, or John Le Carré; Codename Villanelle, The Bourne Identity, I Am Pilgrim, The Secret Agent
Random elements: Lipsticks that turn into guns (these things really existed!), Top secret files/documents, Safes, Sight pictures, Secret codes & Decoders, Typewriters, stolen paintings, perfume, maps/location trackers and wiretapping instruments, keys/keycards, CCTV tapes, fake passports, fingerprint scans, wigs, cocktails