Although I haven't figured out all the clues, the final grid looks something like this
>! [![enter image description here][1]][1]

**1.** Far north Silicon Valley's research & development leaders surround Jessica (8)
>! Svalbard - Alba inside S.V.R & D

**2.** Pop star loses British-American distribution rights to music organization (4)
>! Riaa = Rihanna - hnn

**4.** Clapton song loses heart, gets inside club to be McCartney song (6)
>! Lalula = La(y)la + c**lu**b

**5.** Yale professor Jenny with rights to Diablo north of Mali's capital (8)
>! Lindblom - Lind + blo + M

**6.** In retrospect, Korean Secretary-General is a Swedish actress (5)
>! Noomi - The end of Ban Ki-moon spelled backwards

**7.** Before Christ, Jonah's insiders introduced first Hebrew God (6)
>! Adonai = AD + ona + i

**8.** Excess of vitamins lacking irate vim leads to state of trance (8)
>! Hypnosis - Hypervitaminosis without *irate vim*

**9.** Metric cruise around psychic medium is funny business (6)
>! Sitcom?

**10.** Flamboyant fly's wings around wish-granting body part (6)
>! Flashy = f + lash + y

**11.** Jovial monster rips out heart, surrounding first person (5)
>! Happy?

**13.** Clothing material shelled for Holy Roman emperor (4)
>! Otto = (C)otto(n)

**14.** Taiwanese company contracted Nigerian people (3)
>! Asu = Asus - s

**15.** Ancient piano instrumental finishes grand finale (3)
>! Old = pian**o** instrumenta**l** + gran**d**

**16.** Elizabeth places a wager close to fourth of July (5)
>! Betsy = Bets + y

**17.** Tried architect glances, moves foot to the west (5)
>! Speer = peers with s on the left.

**18.** Ethiopian opera featuring keyboard instrument (5)
>! Piano - Ethio**pian o**pera

**19.** Postal director to turn head with extreme envy (3)
>! Uwe = t**u**rn + **w**ith + **e**nvy

**20.** Bold goer initially heads up inside rural centre (5)
>! Uhura - **h**eads **u**p inside 'ura'

**21.** Army unit with small four-wheeler and wizard (8)
>! Squadron = s + quad + ron

**22.** Standards organization backs network model (3)
>! OSI - ISO backwards

**23.** Boating tool from metallic mineral, reportedly (3)
>! Oar - sounds like ore

**24.** 113 previously used underwater turtle heads (3)
>! Uut - **u**sed **u**nderwater **t**urtle

**25.** Tea and baked goods for unsightly creatures (6)
>! Trolls = T + rolls

**28.** Don't start to hide behind blue-green toxin (7)
>! Cyanide = Cyan + (h)ide

**30.** Heroic poem briefly does make up chapter (7)
>! Episode = Epi(c) + anagram of *does*

**31.** Street goes below tree, never seen before (5)
>! First = Fir + st

**32.** Elizabeth initially next in line, loses turn (5)
>! Queen

**36.** Spice rings encircle half-hearted Ronald (7)
>! Oregano = O + regan + o

**37.** Programming pioneer's top three proverbs (3)
>! Ada

**38.** Deep blue crowdfunding site with no ego (6)
>! Indigo = Indiegogo - ego

**39.**
>! Jodie = Jo + die

**40.** Murderbot Ultra One ultimately scrapped (6)
>! Ultron = Ultr(a) + On(e)

**41.** Back balsam? Ah, a beautiful country (7)
>! Bahamas - bal**sam? Ah, a b**eautiful

**43.** No start for the trip of me and you (3)
>! Our = (T)our

**44.** On the premises, part spins it up (2 4)
>! In situ - sp**ins it u**p

**45.** Legislative organs for storyteller (5)
>! Dumas?

**47.** Māori prophet's revolutionary aura (3)
>! Rua

**49.** Avenge odd appliance manufacturer (3)
>! AEG - **A**v**e**n**g**e

**50.** Vengeful seaman held in Allahabad (4)
>! Ahab - All**ahab**ad

**51.** Cold sea fog from an empty hangar (4)
>! Haar - ha(ng)ar

**54.** Monagan brings up nineties host (6)
>! Nagano = M**onagan** backwards

**57.** Champion checker in the house (3)
>! Hou = **hou**se

**60.** Motor club's credit rating (3)
>! AAA

**61.** Brush a pet in living room (5)
>! Groom - livin**g room**

**62.** Elevated bonus card game (3)
>! Uno - b**onu**s

**63.** Gorilla secretly escapes (3)
>! Ape - esc**ape**s

**64.** Empty spaces for Roombas (7)
>! Vacuums - although vacua is usually the plural

**69.** Melted into Braxton (4)
>! Toni - anagram of *into*

**70.** Car with no sound (5)
>! Audio?


  [1]: https://i.sstatic.net/zlsaA.png