So loo shuns!

Here are the solutions to the cryptic clues.

"~=" represents an anagram/jumble.
"==" represents synonym (approximate)

Note, it arcs carelessly like a sword! (8)*
Note = MI + IT + ARCS, ~= SCIMITAR = kind of sword.

One less person of Spanish origin is an unwanted extra undergrowth. (7)*
Spanish origin = HISPANIC - I (one less) = HSPANIC ~= SPINACH = extra undergrowth (secondary meaning).

Trivial currency cannot buy this sweater! (8)
Trivial = MERE, currency = CASH, CASHMERE

Ha, kick out hundred trousers! (5)
HA, KICK - C (out hundred) = KHAKI

Aquatic plant around the eastern branch of mathematics. (7)
ALG {E. BR.} A

Decapitated citizen is in a peaceful state of mind. (3)
CITIZEN - CITI (head removed) = ZEN

Snake, tangled around a traffic deadlock sleeps in these. (7)~
ASP == snake, a traffic deadlock == A JAM, P{A JAM}AS

A variant is out! (6)*
is out == Not in. A VARIANT - IN ~= AVATAR (a variant).

The "Great Charter" is a fishing vessel without gravity! (9)*
The Great Charter == MAGNA CARTA - G (gravity) ~= CATAMARAN == fishing vessel

Endless chain of a hot beverage. (4)
CHAI (you know me...!)

Maybe, it is the destiny of a thousand kites. (6)
M KITES ~= KISMET == destiny

Strangely, his age is for a man's lighthearted entertainment. (6)
HIS AGE ~= GEISHA == man's lighthearted entertainment

A precept. (5)
precept == SUTRA

Market strange teetotallers asleep in bar. (6)
teetotallers == AA, asleep == Z, BA {Z AA} R == market

Chant in adamant rage! (6)
ada(MANT RA)ge => MANTRA == chant

It hung, go make it work zealously! (4, 2)~
hung go ~= GUNG HO == work zealously (close enough, I guess...)

Fifty thousand go backwards around you, a media person. (5)
L(fifty) GO M (thousand) around U (you)=> MOGUL

Dull aggregate of Chinese food items. (3, 3)
DIM SUM

Music for salvation! (7)
NIRVANA

Greg's wife is the divine law. (6)
DHARMA

Mark a strange consequence. (5)
MARK A ~= KARMA == consequence

A tree potted by a bison, perhaps. (6)
A BISON ~= BONSAI == potted tree

Good badge of rank is an aphrodisiac! (7)*
G(ood) ENSIGN (badge of rank) ~= GINSENG == aphrodisiac

An ascetic is a highly talented child without the Public Relations Dept. (4)~*
highly talented child == PRODIGY - PRD ~= YOGI == ascetic

Two vehicles flank a band of travellers. (7)
CAR{A}VAN == band of travellers

Not seen in Chinese energy! (3)
CHINESE - SEEN (not seen) == CHI

As promised, here is a list of people who solved most or all of the puzzle(s) and guessed the theme (not in any particular order):
Charbee, Pappu, Laddu, Durbha, Nandana, Sumi, Chinni, Vera, Nambu.

Thanks for all the feedback, people! Mucho appreciato.
Now, what I need from everyone is a bunch of ideas for the next theme. Please contribute and make this easier on me.