Stopping the clock without gating the clock
Depends on the flip-flop used in the shift register. Effectively, negate the enable line or assert the disable line :-), but you know that.

I'd ask, "Why not gate clocks, provided that you gate them 'properly'?"

A hazard is that if you asynchronously gate a clock you may (~= 50% chance for a symmetric clock) produce an additional clock transition at disable or re-enable time. ie DO NOT DO THIS



BUT if you gate synchronously so that eg when gate off the clock continues to its next high/low transition, then stays low while still gated off, then when gated on resumes on the next clock low/high edge.
 As described that may allow a very narrow spike at either edge if gating signal just precedes a clock low/ high transition but a bit of common sense in implementation stops that. 

Effectively if delay is acceptable between provided and utilised clock signal (and usually one clock cycle is indistinguishable from the next) then  having a toggling FF in the clock line and disabling it will implement the above (possibly with the described spike hazard present.)



In this circuit from - FPGA Design tips

They say


The following figure shows a synchronous alternative to the gated clock using a data path. The flip-flop is clocked at every clock cycle and the data path is controlled by an enable. When the enable is Low, the multiplexer feeds the output of the register back on itself. When the enable is High, new data is fed to the flip-flop and the register changes its state. This circuit guarantees a minimum clock pulse width and it does not add skew to the clock. The XC4000, Spartan-II, and Virtex families' flip-flops have a built-in clock-enable (CE).






Partially answering my "why not" question above - the gated clock will be delayed by the toggle propogation delay of the gating flip-flop. In some cases this does not matter, in others it's clearly ubbacceptable. The 3rd, worst case, is where it seems OK but sometimes just may not be, on an intermittent basis. So, use with care.

On this page  Roadie Roger warns


Actually gating clocks is relatively evil. Having a gated clock that
transitions less often does save power. Every signal edge is a power
waster in the face of capacitance. Gated clocks create other
problems. Your clocks are no longer exactly lined up. Many chips
have a global clock that goes everywhere. Breaking it into pieces
isn't a good thing. You want to enable data rather than gate clocks.
Call the Enable 'E'. This looks something like:


And Robert usefully counters


Depends on your target technology. The above may hold for FPGA's,
but for standard-cell based ASIC technologies, gated clocks are
an elegant (in my opinion) and clean methodology for low-power
design.

In this case, you will most likely be using a clock tree generator
anyway, and all of the clock tree generators I know easily handle
clock gates. They will automatically align the clocks AFTER any
possible gates, i.e. at the leaf nodes (clock inputs of registers).
In this case, generating a low-skew clock tree is far easier for
gated clocks than for derived clocks (i.e. divided clocks).

Modern synthesis tools also can insert clock gates automatically
by replacing register enables (as shown in the post above) by
gated clocks. This can be handy, but it has the drawback of
reducing your control over clock gates (names, hierarchy).

Inserting clock gates in a VHDL design is easy. Just decide what
gating style you want/need (and/or based, with/without latch, with
test bypass, observability, ...).

My choice is to then explicitly instantiate a clock gating
element where needed. This has the disadvantage of requiring one
to "route" different clock signals through the design, but
it gives you full control over clock gating elements for use
in later stages of the design (clock tree generation, physical
optimization, ...).

Information about "clean" clock gating can be found in books
or also in synthesis tool manuals (where automatic clock
gate insertion is described). Probably you'll also find
resources on the web.