Brocade was a fabric and design with floral symbols invented in Ancient China.
Worn by the Doctor
The Fourth Doctor wore an indigo brocade waistcoat with a fob watch when he met Magnus Greel in London during 1892. (TV: The Talons of Weng-Chiang)
The Sixth Doctor wears a steel blue brocade waistcoat during his Christmas adventure and his encounter with Were Lords. (AUDIO: Blood on Santa's Claw|The Baby Awakes|I Wish It Could Be Christmas Every Day|Brightly Shone The Moon That Night)
The Eighth Doctor wore single-breasted waistcoats of brocade with shawl collars done in wine purple, (AUDIO: He Kills Me, He Kills Me Not,) plain vermillion, (AUDIO: Meanwhile, Elsewhere-Previously, Next Time) or bronze brown. (TV: The Night of the Doctor) His war successor wore the bronze one for some time. (TV: The Night of the Doctor; AUDIO: Light the Flame; WC: Doctors Assemble)
The Ninth Doctor wore an ascot tie of burgundy brocade on 1912 Southampton. (TV: Rose)
The Twelfth Doctor wore an azure blue brocade waistcoat with a high collar during a visit to the 1814 frost fair. (TV: Thin Ice)
The Thirteenth Doctor wore an azure and crimson brocade blouse with frog buttons when she, Yasmin Khan, and Dan Lewis teamed up with Madam Ching and Ji-Hun to defeat renegade Sea Devils including Marsissus round China during 1807. (TV: Legend of the Sea Devils [+])
In his Sixth Doctor form, the Curator wore a single-breasted waistcoat of amber and bronze brocade with a fob watch. (AUDIO: The Artist at the End of Time)
Worn by Companions
Rose Noble wore a crimson and peach brocade blouse during a dinner party. (TV: The Giggle)
Jackson Lake wore a double-breasted waistcoat of scarlet brocade with a shawl collar and a gold fob watch when he and Rosita worked with the Tenth Doctor to stop Cybermen from Pete's World during the 1851 Incident. (TV: The Next Doctor)
Gordon Jago and George Litefoot wore double-breasted waistcoats of brocade. (TV: The Talons of Weng-Chiang)
Worn by the Master
When posing as Professor Yana, the War Master wore a single breast waistcoat of wine purple brocade up to his death. His successor, the Saxon Master, wore it for some time. (TV: Utopia)
Missy, a feminine version of the Master, wore a fern green brocade cravat; (TV: Extremis) right up to her fall after being shot by her predecessor with a laser screwdriver to stop her from helping the Twelfth Doctor to save Mondasians from Cybermen. (TV: The Doctor Falls)
Worn by Others
Robert Muir wore a beige brocade cravat with his tan suit on 1925. (TV: Black Orchid)
Rogue, a bounty hunter, wore a single-breasted waistcoat of royal blue brocade in 1813. (TV: Rogue)
Charles Dickens wore a single breasted waistcoat of ebony and gold brocade when he met the Ninth Doctor, Rose Tyler, Gwyneth, and the Gelth in Cardiff during 1869. (TV: The Unquiet Dead)
Rhys Williams wore a crimson and gold brocade waistcoat when he married Gwen Cooper. (TV: Something Borrowed)
Wrack. the leader of the Eternals on the Buccaneer, wears a bronze brocade vest. (TV: Enlightenment)
The Valeyard wore a copy of the Eighth Doctor's single-breasted waistcoat of bronze paisley-brocade. (AUDIO: The War Valeyard)
Doctor Ogron wore a copy of the Eighth Doctor's double-breasted waistcoat of silver paisley-brocade. (AUDIO: Planet of the Ogrons)